Layerwise computability and image randomness

Laurent Bienvenu; Mathieu Hoyrup; Alexander Shen

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arXiv · 1607.04232

Layerwise computability and image randomness

Laurent Bienvenu·Mathieu Hoyrup·Alexander Shen

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Abstract

Algorithmic randomness theory starts with a notion of an individual random object. To be reasonable, this notion should have some natural properties; in particular, an object should be random with respect to image distribution if and only if it has a random preimage. This result (for computable distributions and mappings, and Martin-L\"of randomness) was known for a long time (folklore); in this paper we prove its natural generalization for layerwise computable mappings, and discuss the related quantitative results.

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BibTeX RIS

Laurent Bienvenu, Mathieu Hoyrup, Alexander Shen. 2016-07-14. Layerwise computability and image randomness. https://arxiv.org/abs/1607.04232

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